Question

Simplify tan9x-tan5x / 1+tan9xtan5x​

Answer 1

The given expressions simplifies to tan (4x).

Explanation:

Here, the given expression is :
`(tan9x - tan5x)/(1+ tan9xtan5x)`

By TRIGONOMETRIC IDENTITY:

`tan (A-B)  = (tanA - tanB)/(1+ tanAtanB)`

Putting this identity here, and taking A = 9 x, B = 5 x, we get

`(tan9x - tan5x)/(1+ tan9xtan5x) = tan (9x-5x)`

= tan(4x)

Hence, the given expressions simplifies to tan (4x).